Two Sum

Problem Statement

Given an array of integers nums and an integer target, return indices of the two numbers such that they add up to target. You may assume that each input would have exactly one solution, and you may not use the same element twice. You can return the answer in any order.

Constraints

• 2 <= nums.length <= 10^4
• -10^9 <= nums[i] <= 10^9
• -10^9 <= target <= 10^9

Approach 1: Using a Hash Map

Time Complexity: O(n)

This approach has linear time complexity because we iterate through the array once and perform constant-time operations (such as checking if an element exists in the hash map).

Flowchart

graph LR
    Start --> Initialize
    Initialize --> Loop
    Loop --> Calculate
    Calculate --> Check{Check if complement exists in hash map}
    Check -- Yes --> Return
    Check -- No --> Store
    Store --> Loop
    Return --> End